Political Economy Pierre Boyer École Polytechnique - CREST Master in Economics Fall 2018 Schedule: Every Wednesday 08:30 to 11:45 Boyer (École Polytechnique) Political Economy Fall 2018 1 / 56
Outline of the class Introduction Lecture 2-5: Tools of political economics with applications Lecture 6: Comparative Politics Part II: Dynamic Political Economy Boyer (École Polytechnique) Political Economy Fall 2018 2 / 56
Bierbrauer and Boyer (2018): Politically feasible reforms of non-linear tax systems Political economy and welfare-maximizing approaches to redistributive taxation: I. Normative analysis of non-linear tax policy: Earnings subsidies for the poor, tax rate for the rich, universal basic income, flat taxes... II. Political economy analysis: Multidimensional policy space no Condorcet winner majority-preferred tax policies difficult to characterize. Boyer (École Polytechnique) Political Economy Fall 2018 3 / 56
Open questions Are optimal tax policies politically feasible? Are politically feasible policies efficient/ welfare-maximizing? Workhorse only for linear income taxation (Roberts, 1977; Meltzer and Richard, 1981). For non-linear taxation, some recent papers based on game-theoretic analyses of the political process. Lack of a broadly accepted conceptual framework for tax reforms. Boyer (École Polytechnique) Political Economy Fall 2018 4 / 56
Overview An analysis of politically feasible and welfare-improving tax reforms: Classical Mirrlees environment with non-linear schedules. Consider reforms of a given status quo in tax policy: - President Woodrow Wilson Inaugural Address (March 1913): We shall deal with our economic system as it is and as it may be modified, not as it might be if we had a clean sheet of paper to write upon; and step by step we shall make it what it should be - The Trump Plan will collapse the current seven tax brackets to three brackets Boyer (École Polytechnique) Political Economy Fall 2018 5 / 56
Median voter theorems for monotonic reforms Monotonic reforms: Tax cuts/ raises a monotonic function of income. Median voter theorems: Given an arbitrary non-linear tax system, a monotonic tax reform is preferred by a majority if / only if it is preferred by the voter with median income. Boyer (École Polytechnique) Political Economy Fall 2018 6 / 56
Characterization of politically feasible reforms Focus on a special class of small monotonic reforms Saezian perturbations, Saez (2001) Welfare implications of such perturbations well understood. We provide a characterization of the political feasibility of Saezian perturbations. Main result: - For incomes below the median: tax cuts politically feasible. - For incomes above the median: tax raises politically feasible. Discontinuity at the median income. Boyer (École Polytechnique) Political Economy Fall 2018 7 / 56
A new look at our tax schedule: puzzle of strong progression of marginal taxes around the median income (a) France: La décote. (b) Germany: middle class belly (Mittelstandsbauch). (c) US phasing out of the EITC. History of tax changes, introduction of income taxes (Scheve and Stasavage, 2010,2016; Aidt and Jensen, 2009), negative marginal tax rates (EITC, Prime d activité, UK Working Tax Credit). Offered reforms of tax schedules during electoral campaigns (Landais et al., 2011; Zoutman et al., 2016). Boyer (École Polytechnique) Political Economy Fall 2018 8 / 56
Extensions 1 Taxation of savings/ Atkinson-Stiglitz (1976)/ Broadening of tax base. 2 Fixed costs of labor-market participation: Saez (2002). 3 Public-good provision/ Benefits-based taxation: Musgrave (1959). 4 Luck vs Effort: Alesina and Angeletos (2005). Multidimensional heterogeneity identity of the median voter depends on the status quo. Boyer (École Polytechnique) Political Economy Fall 2018 9 / 56
Preferences Preferences are represented by a utility function u(c, y, ω): Increasing in c, decreasing in y. Spence-Mirrlees single crossing property: Higher ω flatter indifference curves in a y-c-diagram Earnings monotonic in type under any decentralizable/ incentive compatible allocation. Median type ω M also has median income. Leisure a non-inferior good: indifference curves in a y-c-diagram become, if anything, steeper if individuals receive exogenous income. Boyer (École Polytechnique) Political Economy Fall 2018 10 / 56
Tax reforms I Consumption schedule after a reform: C 1 (y) = c 1 + y T 1 (y), where T 1 (y) = T 0 (y) + τ h(y), c 1 = c 0 + R (τ, h), and T 1 (0) = T 0 (0) = 0, where R (τ, h) is the reform induced change in tax revenue. Boyer (École Polytechnique) Political Economy Fall 2018 11 / 56
Tax reforms II I.e. basic income absorbs changes in tax revenues. Consider alternative uses of tax revenue in extensions. Represent a generic reform as a pair (τ, h). Boyer (École Polytechnique) Political Economy Fall 2018 12 / 56
Tax reforms III Monotonic reforms: A tax reform (τ, h) is said to be monotonic over a range of incomes Y R + if T 1 (y) T 0 (y) = τ h(y) is a monotonic function for y Y. A reform is monotonic above (below) the median if T 0 (y) T 1 (y) = τ h(y) is a monotonic function for incomes above (below) the median income. Example: Reforms in the (τ, y a, y b )-class/ Saezian reforms: 0, if y y a, h(y) = y y a, if y a < y < y b, y b y a, if y y b. Boyer (École Polytechnique) Political Economy Fall 2018 13 / 56
Total number of possible reforms (#years*#countries): 528 Total number of reforms: 394 Number of monotonic reforms: 309 (78%) Number of non-monotonic reforms: 85 (22%) Table: Summary statistics on the tax reforms for a panel of 33 OECD countries (2000-2016). Boyer (École Polytechnique) Political Economy Fall 2018 14 / 56
First year of income taxes: 1916 Total number of possible reforms until 2016: 100 Total number of reforms until 2016: 74 Number of monotonic reforms: 62 (84%) Number of non-monotonic reforms: 12 (16%) Table: Summary statistics on the history of French tax reforms (1916-2016). Boyer (École Polytechnique) Political Economy Fall 2018 15 / 56
Figure: Reform of the French income tax in 1937 Boyer (École Polytechnique) Political Economy Fall 2018 16 / 56
Figure: Important reforms in France T1-T0 T1-T0 600 5000 50 000 100 000 150 000 200 000 250 000 y 400 300 000-5000 200-10 000-15 000 20 000-20 000-25 000 40 000 60 000 80 000 100 000 120 000 y 140 000-200 The reforms were implemented in years 2013 (dark blue), 2007 (purple), 2004 (brown), 2003 (green), and 2002 (blue). The figure (right panel) shows the reform implemented in year 2011. Boyer (E cole Polytechnique) Political Economy Fall 2018 17 / 56
Beginning of examination: 1981 Total number of possible reforms until 2016: 35 Total number of reforms until 2016: 35 Number of monotonic reforms: 28 (80%) Number of non-monotonic reforms: 7 (20%) Table: Summary statistics on the tax reforms in the United States (1981-2016). Boyer (École Polytechnique) Political Economy Fall 2018 18 / 56
Figure: Important reforms of the US income tax: 1993 and 2013 1500 6000 1000 4000 T1-T0 1993-1992 500 T1-T0 2013-2012 2000 0 ytax 50000 100000 0 ytax 100000 200000 300000 400000 500000-500 -2000 Boyer (École Polytechnique) Political Economy Fall 2018 19 / 56
Figure: Important reforms of the US income tax: 1987 0 ytax 100000 200000 300000 400000 500000 0 ytax 10000 20000 30000-20000 -200 T1-T0 1987-1986 T1-T0 1987-1986 -40000-400 -600-60000 Boyer (École Polytechnique) Political Economy Fall 2018 20 / 56
Preliminaries Let y (e, τ, ω) := argmax y u(c 0 + e + y T 0 (y) τh(y), y, ω). Corresponding indirect utility denoted by V(e, τ, ω). Status quo earnings: Define ỹ 0 : Ω R + with ỹ 0 (ω) = y (0, 0, ω). Assumption 1. The function ỹ 0 is strictly increasing and, for all ω, characterized by the first order condition u c ( )(1 T 1 (y)) + u y( ) = 0. Rules out a status quo with bunching. Relaxed in the Appendix. Reform-induced change in tax revenue: R (τ, h) = ω ω {T 1 (y ( R (τ, h), τ, ω)) T 0 (y (0, 0, ω))}f (ω) dω. Boyer (École Polytechnique) Political Economy Fall 2018 21 / 56
Terminology: V (ω τ, h) is the reform-induced change in indirect utility. Pareto-improving reforms. For all ω Ω, V (ω τ, h) 0, strict for some ω Ω. Welfare-improving reforms. W (g τ, h) := ω Politically feasible reforms. S(τ, h) := ω ω ω g(ω) V (ω τ, h)f (ω) dω > 0. 1{ V (ω τ, h) > 0}f (ω) dω 1 2. Boyer (École Polytechnique) Political Economy Fall 2018 22 / 56
Small reforms I An individual of type ω benefits from a marginal increase of a small if, at τ = 0, V τ (ω τ, h) := d dτ V( R (τ, h), τ, ω) > 0. Theorem 1 Let h be a monotonic function. The following statements are equivalent: 1 The median voter benefits from a small reform. 2 There is a majority of voters who benefit from a small reform. Extensions to large reforms in the paper. Boyer (École Polytechnique) Political Economy Fall 2018 23 / 56
Small reforms II R IC L τ Boyer (École Polytechnique) Political Economy Fall 2018 24 / 56
Small reforms III R IC H IC L R τ τ Boyer (École Polytechnique) Political Economy Fall 2018 25 / 56
Interpretation: Median voter theorem holds if preferences over policies satisfy a single-crossing condition, see Rothstein (1990,1991) and Gans and Smart (1996). Consider preferences over policies in a (τ, R )-space; denote by s(τ, R, ω) slope of indiff. curve through (τ, R ). Lemma For any ω and any point (τ, R ), s(τ, R, ω) = h(y (τ, R, ω)). Median voter theorem follows from a single-crossing condition: At any point in (τ, R )-space, higher types have steeper indifference curves. Boyer (École Polytechnique) Political Economy Fall 2018 26 / 56
Corollary 1 Let h be a non-decreasing function. 1 A small reform with τ > 0 is Pareto-improving iff V τ (ω 0, h) 0. 2 A small reform (τ, h) with τ < 0 is Pareto-improving iff V τ (ω 0, h) 0. 3 A small reform with τ > 0 benefits voters in the bottom x per cent and harms voters in the top 1 x per cent iff V τ (ω x 0, h) = 0. Boyer (École Polytechnique) Political Economy Fall 2018 27 / 56
Weakening the monotonicity requirement Proposition 1 Let ỹ 0M be median income in the status quo. 1 Let h be non-decreasing for y ỹ 0M. If the median voter benefits from a small reform with τ < 0, then it is politically feasible. 2 Let h be non-decreasing for y ỹ 0M. If the poorest voter benefits from a small reform with τ < 0, then it is politically feasible. Boyer (École Polytechnique) Political Economy Fall 2018 28 / 56
Weakening the monotonicity requirement Proposition 2 Let ỹ 0M be median income in the status quo. 1 Let h be non-decreasing for y ỹ 0M. If the median voter benefits from a small reform with τ > 0, then it is politically feasible. 2 Let h be non-decreasing for y ỹ 0M. If the richest voter benefits from a small reform with τ > 0, then it is politically feasible. Boyer (École Polytechnique) Political Economy Fall 2018 29 / 56
Boyer (École feasible. Polytechnique) Political Economy Fall 2018 30 / 56 Detecting politically feasible reforms From now on: Focus on reforms in the (τ, y a, y b )-class. Theorem 2 Suppose that T 0 is an interior Pareto-optimum. (i) For y 0 < ỹ 0M, there is a small reform (τ, y a, y b ) with y a < y 0 < y b and τ < 0 that is politically feasible. (ii) For y 0 > ỹ 0M, there is a small reform (τ, y a, y b ) with y a < y 0 < y b and τ > 0 that is politically feasible. Within Pareto bounds, for incomes below the median, lower taxes are politically feasible. for incomes above the median, higher taxes are politically
Revenue-increasing reforms I Notation: Ĩ 0 (ω ) := E [ T 0 (ỹ0 (ω )) y e (0, 0, ω ) ω ω ]. Proposition 3: Laffer bound/ Upper Pareto bound Let D up (y ) := 1 F( ω0 (y )) f ( ω 0 (y )) ( ) 1 Ĩ 0 ( ω 0 (y y )) ω (0, 0, ω 0 (y )) y τ(0, 0, ω 0 (y )). Suppose that there is an income level y so that T 0 (y ) > D up (y ). Then there exists a revenue-increasing reform (τ, y a, y b ) with τ < 0, and y a < y < y b. Boyer (École Polytechnique) Political Economy Fall 2018 31 / 56
Revenue-increasing reforms II Note: Characterization in terms of the derivatives of the earnings function y. Boyer (École Polytechnique) Political Economy Fall 2018 32 / 56
Revenue-increasing reforms III Notation: [ ] Ĩ 0 (ω ) = E T 0 (ỹ0 (ω)) ỹ0 (ω) η 0 (ω) ω ω c 0 where η 0 (ω) is the elasticity of type ω s earnings with respect to the intercept of the consumption schedule. ε 0 (ω): elasticity of type ω s earnings with respect to the net-of-tax rate 1 T ( ) and with respect to the skill index ω, Boyer (École Polytechnique) Political Economy Fall 2018 33 / 56
Revenue-increasing reforms IV Corollary 2: Sufficient statics formula for upper Pareto bound Let D up (y ) := 1 F( ω0 (y )) f ( ω 0 (y )) ω 0 (y ) ( ) 1 Ĩ 0 ( ω 0 (y α )) 0 ( ω 0 (y )) ε 0 ( ω 0 (y )). Suppose there is an income level y T 0 so that (y ) 1 T 0 (y ) > D R (y ). Then there exists a tax-revenue-increasing reform (τ, y a, y b ) with τ < 0, and y a < y < y b. If quasi-linear iso-elastic utility (ETI: ɛ): Boyer (École Polytechnique) Political Economy Fall 2018 34 / 56
Revenue-increasing reforms V D up (y ) = 1 F Y(y ) f Y (y ) y 1 ɛ, Boyer (École Polytechnique) Political Economy Fall 2018 35 / 56
Revenue-increasing reforms VI Remarks: 1 Income effects Sufficient statistics depend on the status quo Recall that income effects and the status quo schedule enter via [ ] Ĩ 0 (ω ) = E T 0 (ỹ0 (ω)) ỹ0 (ω) η 0 (ω) ω ω c 0 2 Sufficient statistics without income effects = Solution to a relaxed problem of revenue-maximizing income taxation = Solution to relaxed Rawlsian/ maximin problem, see Brett and Weymark (2016)., Boyer (École Polytechnique) Political Economy Fall 2018 36 / 56
Revenue-increasing reforms VII T 0 1 T 0 D R ( ) 1 a 1 + 1 ɛ y e y t y Figure: Sufficient statistics for revenue-increasing reforms Boyer (École Polytechnique) Political Economy Fall 2018 37 / 56
Revenue-increasing reforms VIII 2.5 2.0 2.0 1.5 1.5 T'/(1 T') T'/(1 T') 1.0 1.0 0.5 0.5 0 100,000 200,000 300,000 400,000 Taxable income 0 100,000 200,000 300,000 400,000 Taxable income Figure: Upper Pareto bounds for the US income tax in 2012 Figure 6 relates the upper Pareto bounds D up (dashed line) to the US income tax system in 2012. The figure on the left is drawn for an ETI of 1.2, the figure on the right for an ETI of 1.4. Boyer (École Polytechnique) Political Economy Fall 2018 38 / 56
Revenue-increasing reforms IX 2.5 2.0 2.0 1.5 1.5 T'/(1 T') T'/(1 T') 1.0 1.0 0.5 0.5 0 100,000 200,000 300,000 400,000 Taxable income 0 100,000 200,000 300,000 400,000 Taxable income Figure: Upper Pareto bounds for the US income tax in 2013 Figure 7 relates the upper Pareto bounds D up (dashed line) to the US income tax system in 2013. The figure on the left is drawn for an ETI of 1.2, the figure on the right for an ETI of 1.4. Boyer (École Polytechnique) Political Economy Fall 2018 39 / 56
Pareto-improving tax raises I Proposition 4: Lower Pareto bound Let D low 1 (y) := f ( ω 0 (y)) {( 1 Ĩ 0 ( ω 0 ) (y)) F( ω 0 (y)) + (Ĩ0 ( ω 0 )} y (y)) I ω (0, 0, ω 0 (y)) 0 y τ (0, 0, ω0 (y)). Suppose that there is an income level y such that T 0 (y ) < D low (y ). Then there exists a Pareto-improving reform (τ, y a, y b ) with τ > 0, and y a < y 0 < y b. Boyer (École Polytechnique) Political Economy Fall 2018 40 / 56
Pareto-improving tax raises II Observations: Negative if ω close to ω, or if there are no income effects. Bound on earnings subsidies. If such subsidies are too large, then lowering them is Pareto-improving. No income effects D P = solution of a relaxed maximax-problem, see Brett and Weymark (2016). If quasi-linear iso-elastic utility: D low (y ) = F Y(y ) f Y (y ) y 1 ɛ, Boyer (École Polytechnique) Political Economy Fall 2018 41 / 56
Pareto-improving tax raises III T 0 1 T 0 y e y t y D P Figure: Sufficient statistics for Pareto-improving reforms Boyer (École Polytechnique) Political Economy Fall 2018 42 / 56
Pareto-improving tax raises IV 0.0 0.0 0.5 0.5 T'/(1 T') T'/(1 T') 1.0 1.0 1.5 1.5 5,000 10,000 15,000 20,000 Taxable income 5,000 10,000 15,000 20,000 Taxable income Figure: Lower Pareto bounds for the US income tax in 2012 Figure 9 relates the lower Pareto bounds D low (dotted line) to the US income tax system in 2012 for an ETI of 1.2. The figure on the left is drawn for the statutory schedule taken from the OECD database and the one on the right represents the full schedule Boyer (École Polytechnique) Political Economy Fall 2018 43 / 56
Pareto-improving tax raises V with earning subsidies (EITC) for singles without dependents taken from the NBER TAXSIM database. Boyer (École Polytechnique) Political Economy Fall 2018 44 / 56
Politically feasible reforms I Proposition 5 1 Let y < ỹ 0M and T 0 (y ) > D low (y ). Then there is a politically feasible reform (τ, y a, y b ) with τ < 0, and y a < y < y b. 2 Let y > ỹ 0M and T 0 (y ) < D up (y ). Then there is a politically feasible reform (τ, y a, y b ) with τ > 0, and y a < y < y b. Boyer (École Polytechnique) Political Economy Fall 2018 45 / 56
Politically feasible reforms II T 0 (y) 1 T 0 (y) D M y e y t y Figure: Sufficient statistics for politically feasible reforms Boyer (École Polytechnique) Political Economy Fall 2018 46 / 56
Politically feasible reforms III Interpretation: Discontinuity of politically feasible reforms at the median level of income: - Tax cuts politically feasible for incomes below the median - Tax raises politically feasible for above median incomes Possible explanation for strong increase of marginal rates close to the median income in actual tax policy. Starting from laissez-faire: - The introduction of earnings subsidies for the poor is politically feasible. - The introduction of positive marginal tax rates for the rich is politically feasible. Boyer (École Polytechnique) Political Economy Fall 2018 47 / 56
Politically feasible reforms IV -1000 0 1000 2000 3000 4000 Taxable income 10000 20000 30000 40000-2000 0 2000 4000 6000 Taxable income 10000 20000 30000 40000 Figure: Income tax schedules for singles without dependants from micro-simulation models for the US (left figure) and France (right figure) in 2012 Boyer (École Polytechnique) Political Economy Fall 2018 48 / 56
Politically feasible welfare improvements I Proposition 6: Welfare-improving reforms Let D W g (y) := 1 F( ω0 (y)) f ( ω 0 (y)) where Φ 0 (ω) := 1 Ĩ 0 (ω) (1 I 0 ) Γ 0(ω) γ 0. Φ 0 ( ω 0 (y)) y ω(0, 0, ω 0 (y)) y τ(0, 0, ω 0 (y)), 1 Suppose there is an income level y so that T 0 (y ) < D W g (y ). Then there exists a welfare-increasing reform (τ, y a, y b ) with τ > 0, and y a < y < y b. 2 Suppose there is an income level y so that T 0 (y ) > D W g (y ). Then there exists a welfare-increasing reform (τ, y a, y b ) with τ < 0, and y a < y < y b. Boyer (École Polytechnique) Political Economy Fall 2018 49 / 56
Politically feasible welfare improvements II Proposition 7 1 Let y < ỹ 0M and T 0 (y ) > Dg W (y ). Then there is a politically feasible and welfare-improving reform (τ, y a, y b ) with τ < 0, and y a < y < y b. 2 Let y > ỹ 0M and T 0 (y ) < Dg W (y ). Then there is a politically feasible reform (τ, y a, y b ) with τ > 0, and y a < y < y b. Boyer (École Polytechnique) Political Economy Fall 2018 50 / 56
Politically feasible welfare improvements III T 0 1 T 0 D M D W g y e y t y Boyer (École Polytechnique) Political Economy Fall 2018 51 / 56
Politically feasible welfare improvements IV Figure: Sufficient statistics for politically feasible and welfare-improving reforms Boyer (École Polytechnique) Political Economy Fall 2018 52 / 56
Politically feasible welfare improvements V Implications: Starting from laissez faire, above the median, tax increases welfare-improving and politically feasible. below the median, tax increases welfare-improving but not politically feasible, earnings subsidies politically feasible but welfare-damaging. Why? Welfare calls for positive marginal taxes in the canonical Mirrlees-model. Boyer (École Polytechnique) Political Economy Fall 2018 53 / 56
Politically feasible welfare improvements VI Welfare considerations dampen the effects of political feasibility: call for lower marginal tax rates at the top and higher marginal tax rates at the bottom than the requirement of political feasibility. Boyer (École Polytechnique) Political Economy Fall 2018 54 / 56
Summary: Politically feasible reforms in the (τ, y a, y b )-class Methodologically: Conditions for revenue-increasing, Pareto-improving, welfare-improving or politically feasible reforms. Conditions take the form of sufficient statistics formulas. Diagnosis system for tax reforms Substantively: Discontinuity of schedule for politically feasible reforms at the median level of income. Within Pareto bounds, tax cuts for the poor and tax raises for the rich are politically feasible. Boyer (École Polytechnique) Political Economy Fall 2018 55 / 56
Outline of the class Introduction Lecture 2-5: Tools of political economics with applications Lecture 6: Comparative Politics Part II: Dynamic Political Economy Boyer (École Polytechnique) Political Economy Fall 2018 56 / 56